Question

# A bullet of mass a and velocity b is fired into a large block of wood of mass c, what is the final velocity of the system?

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Solution

## Step 1: GivenMass of the bullet$=a$Initial velocity of the bullet$=b$Mass of the wood$=c$Step 2: Determine the initial momentumLet the initial momentum be ${M}_{i}$${M}_{i}=mass×initialvelocity\phantom{\rule{0ex}{0ex}}=ab$Step 3: Determine the final momentumLet the final velocity be $v$ and the final momentum be ${M}_{f}$ ${M}_{f}=massofbulletinwood×finalvelocity\phantom{\rule{0ex}{0ex}}=\left(a+c\right)v$ Here, both the mass of the bullet and the mass of wood are considered as the bullet enters the wooden blockStep 4: Determine the final velocityAccording to the law of conservation of momentum, the initial momentum will be equal to the final momentum. ${M}_{i}={M}_{f}\phantom{\rule{0ex}{0ex}}ab=\left(a+c\right)v\phantom{\rule{0ex}{0ex}}v=\frac{ab}{\left(a+c\right)}$Therefore, the final velocity of the system is $v=\frac{ab}{\left(a+c\right)}$

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